A disclaimer: I haven't yet used the BMW model myself, and might miss some otherwise obvious problems.

On to your minimization:
1- By default GROMACS sets its convergence force threshold to 10, but Martini simulations can be started from configurations with much higher forces (it is also very unlikely to ever get such low minimized force values). That note is safe to ignore.

2- The maximum force of the order of 10^3 is also at the limit of what's acceptable for starting a Martini run.

3- Indeed, as you remark, the potential energy isn't negative, and that yes is a problem. Let's try solving it:
- You give very few details on how you are using this system. I assume you are using the .itp, .mdp, and .xvg files at the URL you got the structure from.
- Also, you must use an index to tell GROMACS what is solvent and what is not. Groups SOL and NON must be defined in this index file.
- Finally, at the end of "martini_v2.1_bmw.itp" you'll find the description of the water model. You'll see it is modeled as a triangle constrained with the SETTLE scheme. This doesn't minimize very well, and the model authors include an alternative representation to be used for minimization. Make sure you use this alternative model **but only for minimization**.

Thanks for the reply, Manel. I figured out what was going wrong. I had to incorporate the tabulated potentials provided on the website of the developers. Using Gromacs non-bonded types was what was leading to the unstability in the system.